The couple were attending the inaugural Tusk Conservation Awards, celebrating the work of wildlife conservationists, on the day that the Duke announced he was leaving the Armed Forces to concentrate, in part, on protecting endangered species.

In a speech during the event at the Royal Society, the Duke said: “As you might have gathered, Catherine and I have recently become proud parents – of a baby who has a voice to match any lion’s roar!

“This is actually our first evening out without him, so please excuse us if you see us nervously casting cheeky glances at our mobile phones to check all is well back home.”

Turning to the theme of the awards, he went on: “Like any new parents, our thoughts inevitably turn to the world that our child will inherit. It is unfathomable to imagine a world in which children who have been born in the past couple of months may grow up in a world in which rhinoceros have ceased to live in the wild.”

The Duke and Duchess of Cambridge on their first evening out without Prince George. (DANNY E MARTINDALE/GETTY IMAGES)

He said that in the past year 35,000 elephants were killed for their ivory, a statistic he described as “truly scary”.

He went on: “The possibility of extinction is bad enough for one of our children growing up here in the West, who will never experience the magic of seeing a rhino; or even for my own little George, who Catherine and I very much hope to introduce to east Africa – a place we know and love – in the fullness of time.

“But for a child growing up in Africa and whose birth-right and economic inheritance these creatures are, it is nothing more than immoral that he or she may never experience what his parents and grandparents knew and treasured.”

The royal couple are greeted as they arrive for the awards. (MATT DUNHAM/AP)

It was only the second public engagement for the Duchess since she gave birth in July. Last month she made a surprise appearance by her husband’s side as they started a coastal marathon on Anglesey.

Charles Mayhew, founder of Tusk, of which the Duke is patron, said the Duke was “really excited” about the awards ceremony.

He said: “You have seen tonight the passion he has for conservation. He has had that since he became patron of Tusk in 2005.

“Since the birth of Prince George, like all new parents, you tend to take stock and look at the world in a different light and think about what are we leaving our children, what is the legacy.”

He added: “We arranged this date even before the Duchess became pregnant, so it is completely fortuitous that we have the Duchess here for her first night out since the baby was born and on the day that the Duke has made such a big announcement about his future.”

The winners of the two awards were Tom Lalampaa, of the Northern Rangelands Trust in Kenya, who won the Conservation in Africa award for his work protecting elephants and Clive Stockil, of the Save Valley Conservancy in Zimbabwe, who took the Prince William Award for Conservation in Africa.